The morphogenesis of molluscan shells: A mathematical account using biological parameters

Abstract

In attempts to account mathematically for the morphogenesis of biological structures it is important that the parameters chosen for the purpose should be "biological," that is, they should refer directly to the growth processes through which the structure is formed. Molluscan shells are formed by accretional growth at the mantle edge, and the parameters used for the mathematical description of their formation should therefore refer to events taking place there. In the best of previous attempts to solve this problem, two out of three form parameters have met with this demand, but it was not possible to eliminate beta, half the apical angle of the cone on which lie the centers of successive whorls. It is shown here that beta may be eliminated for many forms of molluscan shells, and when this is not the case beta may indeed be referred to processes taking place at the mantle edge.

The Algorithmic Beauty of Sea Shells

“…Other mathematically equivalent families of parameters have been described in the literature (for example, see Cortie, 1989, Lovtrup andLovtrup, 1988). Other mathematically equivalent families of parameters have been described in the literature (for example, see Cortie, 1989, Lovtrup andLovtrup, 1988).…”

Phylogeny of the Cardiidae (Mollusca, Bivalvia): Protocardiinae, Laevicardiinae, Lahilliinae, Tulongocardiinae subfam. n. and Pleuriocardiinae subfam. n.

“…Therefore, a character state tree can be constructed for this character. Although there have been several attempts to describe the ontogeny of bivalve shell shape (Raup 1966;L0vtrup & L0vtrup 1988;Checa 1991;Johnston et al 1991;Ackerly 1992a, b), a rigorous method of converting morphometric information on bivalve ontogeny into cladistic character states remains to be invented. Therefore, the various shell shapes exhibited by the cardiids covered in this study have been placed in six different states, each of which can be described semi-quantitatively.…”

Theoretical Modelling of the Molluscan Shell: What has been Learned From the Comparison Among Molluscan Taxa?

“…Building on previous studies raising the issue of growth timing in mollusc shells (Løvtrup and Løvtrup 1988;Hutchinson 1990), Rice (1998) framed his hypotheses with reference to relative and absolute shell growth rates. In this model, the shell is simulated in a similar manner as fixed-frame generating curve models.…”